Merge templates with 14C, C, and N data
Radiocarbon analyses for the 2001 samples were not run originally, but were completed on archived samples in 2020.
Fig. 11. Mean profile \(\Delta\)14C for 2001 samples
Caption: Mean \(\Delta\)14C by depth for each site in 2001. Error bars show ±1 standard deviation, solid vertical line shows \(\Delta\)14C of the atmosphere in the year of sampling.
Fig. 11. Profile \(\Delta\)14C for 2009 samples
Caption: Profile \(\Delta\)14C by depth for each site in 2009. Solid vertical line shows \(\Delta\)14C of the atmosphere in the year of sampling. Error bars not shown as only a single replicate profile was analyzed per site.
Fig. 11. Mean profile \(\Delta\)14C for 2019 samples
Caption: Mean \(\Delta\)14C by depth for each site in 2019. Error bars show ±1 standard deviation, solid vertical line shows \(\Delta\)14C of the atmosphere in the year of sampling.
Fig. 11. Mean profile \(\Delta\)14C for 2001 and 2019 samples
Caption: Mean \(\Delta\)14C by depth for each site in 2001 and 2019. Error bars show ±1 standard deviation. Vertical lines show \(\Delta\)14C of the atmosphere in 2001 (solid) and 2019 (dashed).
Fig. 11. \(\Delta\)14C-CO2 of 2019 bulk soil incubations
Caption: \(\Delta\)14CO2 by depth for each site in 2019. One rep from GRrf 10-20 (the 10-20 cm increment sample from the cold granite site) is strongly depleted relative to the other rep: \(\Delta\)14C-CO2 = -396.7, -23.5. The highly depleted sample has been excluded for display reasons.
Fig. 11. \(\Delta\)14C-CO2 of 2001 bulk soil incubations
Caption: \(\Delta\)14CO2 by depth for each site in 2001. Note that some sites only have two depth increments. Similar to the 2019 dataset, one of the GRrf reps from the deepest depth increment was strongly depleted: \(\Delta\)14C-CO2 = -469.1. Both points have been excluded for display reasons.
Fig. 11. \(\Delta\)14C-CO2 of 2001 and 2019 bulk soil incubations
Caption: \(\Delta\)14CO2 by depth for each site in 2001 and 2019. Different depth increments were sampled in 2001 and 2019. Points are the mean of laboratory duplicates; error bars are the measured values of each duplicate. Granite/cold point exlcuded for display reasons as it is strongly depleted.
Fig. 11. \(\Delta\)14C of 2019 bulk soil incubations and corresponding bulk soil
Caption: \(\Delta\)14C of bulk soil and respired CO2 by depth for each site in 2019. Error bars show one standard deviation for bulk soil, points show mean of three replicate profiles for bulk soils and single observations for respired CO2.
Fig. 11. \(\Delta\)14C of 2001 bulk soil incubations and corresponding bulk soil
Caption: \(\Delta\)14C of bulk soil and respired CO2 by depth for each site in 2001. Points show mean of three replicate profiles for bulk soils and mean of laboratory duplicates for respired CO2. The incubated soil samples are a composite made by homogenizing subsamples from each of the three replicate profile samples by depth. Error bars show one standard deviation for bulk soil and the measured values from laboratory duplicates of the incubated composite samples.
Call:
lm(formula = d14c_mean.inc ~ d14c_mean.bulk * PM, data = sra.all.sum.df)
Residuals:
Min 1Q Median 3Q Max
-236.293 -19.975 -1.961 26.546 117.158
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 71.7999 14.7331 4.873 1.46e-05 ***
d14c_mean.bulk 0.5137 0.2831 1.814 0.0764 .
PMBS -22.4831 20.6981 -1.086 0.2833
PMGR -101.3128 22.2944 -4.544 4.27e-05 ***
d14c_mean.bulk:PMBS 0.3595 0.4366 0.823 0.4147
d14c_mean.bulk:PMGR 0.9907 0.3771 2.627 0.0118 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 56.87 on 44 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared: 0.537, Adjusted R-squared: 0.4844
F-statistic: 10.21 on 5 and 44 DF, p-value: 1.542e-06
Fig. 11. Regression of 2019 bulk soil incubations and corresponding bulk soil \(\Delta\)14C
Caption: Regressions of \(\Delta\)14C of bulk soil and respired CO2 by depth for each site in 2019. Error bars show one standard deviation for bulk soil, points show mean of three replicate profiles for bulk soils and single observations for respired CO2.
Fig. 11. Time series of \(\Delta\)14C by depth, as measured
Caption: Points show mean of three profile replicates for 2001, 2009, and 2019 samples. Error bars show ± 1 standard deviation of the mean (only a single profile was analyzed in 2009).
Soils collected in both the 2001 and 2009 sampling campaigns were sampled by horizon, but the depth intervals differed between the two sampling years. In 2009, full profiles were excavated for each site, as opposed to the shorter profiles collected in 2001 from the GR and AN sites. Radiocarbon was measured on all three replicate profiles at each site for the 2001 samples, but only for one of the replicate profiles at each site in 2009, e.g. ANpp rep2, etc.
In order to compare the radiocarbon profiles between 2001, 2009, and 2019 we first interpolated both radiocarbon and carbon stock data at 1 cm intervals for each site in the datasets from each year. The carbon-stock-weighted radiocarbon values for any given target depth interval can then be calculated as a simple sum of the product of the carbon weight of each 1 cm increment (relative to the total carbon stock of the target depth interval) and its radiocarbon value. A monotonic cubic spline fit was used for the carbon stock interpolation (Wendt and Hauser 2013), and a mass-preserving spline was used to fit the radiocarbon data (Bishop, T.F.A., McBratney, A.B., Laslett, G.M., (1999) Modelling soil attribute depth functions with equal-area quadratic smoothing splines. Geoderma, 91(1-2): 27-45).
Fig. 11. Time series of bulk soil \(\Delta\)14C by depth (2001, 2009, 2019)
Caption: Points for 2001 samples show the mean \(\Delta\)14C values at the measured depths. Points for 2009 and 2019 samples are spline-fitted estimates of \(\Delta\)14C predicted for the same depth intervals as measured in 2001. Error bars show ± 1 standard deviation of the mean of three replicate profiles for 2001 and 2019 samples (only a single profile was analyzed in 2009).
Fig. 11. Time series of bulk soil \(\Delta\)14C by depth (splined to 2019 depths)
Caption: Points for 2019 samples show the mean \(\Delta\)14C values at the measured depths. Points for 2001 and 2009 samples are spline-fitted estimates of \(\Delta\)14C predicted for the same depth intervals as measured in 2019. Error bars show ± 1 standard deviation of the mean of three replicate profiles for 2001 and 2019 samples (only a single profile was analyzed in 2009). NB: Only two depth intervals were measured at the cool and cold andesite sites (max depth of 27 and 28 cm, respectively), so linear extrapolation (using the slope of the last 1cm spline-fitted depth increment) was used to extend the profiles to 30 cm.
$`10`
$`20`
$`30`
Fig. 11. Change in \(\Delta\)14C of bulk soil (panel a) and respired CO2 (panel b) over time relative to the atmosphere
Caption: Points for 2019 samples show the mean \(\Delta\)14C values at the measured depths. Points for 2001 and 2009 (bulk only) samples are spline-fitted estimates of \(\Delta\)14C predicted for the same depth intervals as measured in 2019. Error bars for bulk samples in panel (a) show ± 1 standard deviation of the mean of three replicate profiles for 2001 and 2019 samples (only a single profile was analyzed in 2009); error bars for incubation samples in panel (b) show the values of the two reps, while the point represents the mean. NB: Only two depth intervals were measured at the cool and cold andesite sites (max depth of 27 and 28 cm, respectively), so linear extrapolation (using the slope of the last 1cm spline-fitted depth increment) was used to extend the profiles to 30 cm.
The goal of this modeling exercise is to see how parent material and climate/ecosystem affect estimates of soil carbon ages and transit times. Bulk soil 14C observations from 2001, 2009, and 2019 will be used to constrain the carbon models, as well as observations of 14C-CO2 from laboratory soil incubations of soils collected in 2001 and 2019. Previous work has indicated that the carbon stocks at these sites is likely at equilibrium, so we will apply the steady-state assumption to the modeling.
One pool models have been shown repeatedly to be inadequate for describing soil carbon dynamics. However, as simple models are easier to constrain, we will start with a two-pool parallel and two-series models, as these are the simplest model system beyond the single pool approach.
The two-pool parallel model requires the following parameters: * decomposition constants for each pool (k1, k2) * input partitioning coefficient (\(\gamma\)) * steady-state carbon stocks (C) * inputs (I) * initial values of 14C 1 The two-pool series model requires the following parameters: * decomposition constants for each pool (k1, k2) * transfer coefficient (\(\alpha\)) * steady-state carbon stocks (C) * inputs (I) * initial values of 14C
Decomposition rates (k) are related to the amount of 14C in a pre-bomb system (fraction modern, F) at steady-state by the following equations (cf. Schuur, Druffle, and Trumbore, 2016): >Eq. 1
\[F = \frac{k}{k + \lambda}\] >Eq. 2
\[k = \frac{\lambda \cdot F}{1 - F}\] >where \(\lambda\) is the radioactive decay constant (1/8267).
As the decomposition rates will vary, the initial 14C content can be determined dynamically with equation 1.
Carbon stocks are known, while inputs will be estimated and are related to the steady-state conditions by the following equation: >Eq. 3
\[I = (k_{1} \cdot C_{1}) + (k_{2} \cdot C_{2})\] >where C1 and C2 are the carbon stocks of the two model pools.
Both stocks and inputs can be scaled to the known value of the total carbon pool once the steady-state parameters (k1, k2, and \(\gamma\) or \(\alpha\)) have been determined. Pool sizes are a function of the inputs and input partitioning coefficient at steady-state.
A Monte-Carlo Markov chain approach will be used for parameter estimation in combination with an initial optimization algorithm to determine the best set of initial parameters.
Initial model fitting was performed for both model structures using generous parameter ranges [0, 1] for all three parameters (k1, k2, \(\gamma\) or \(\alpha\)). The initial parameter set was found by fitting the models by eye, followed by optimization with the function “modFit” (R package FME), using the Nelder-Mead algorithm. The best set of parameters found by modFit was then used as the input to a Monte Carlo Markov Chain (MCMC), using the function “modMCMC” (R package FME). The number of iterations for the MCMC optimization was set at 5000 intially, with delayed rejection employed to increase efficiency.
The sum of the mean squared error for the best parameter set was slightly lower for the parallel structure than for the series structure. Additionally, the overall mean error of the residuals was also lower for the parallel structure, moderately so for the bulk C observations but substantially so for the respiration observations (in andesite and granite soils in particular).
However, these initial fits yielded unrealistic parameter estimates for multiple sites, particularly at the lower depths. Additionally, the modFit output showed very high correlation between the parameters for both model structures (slightly higher for the two-pool series model).
Optimizing the parameter set requires imposing costs and optionally constraining the allowable range of values for each parameter. Given that we only have data for three time points, this is a relatively sparse data set for constraining these models. Accordingly, the optimization procedure will benefit from a priori constraints of the allowable parameter ranges. For example, since we assume that the system cannot be adequately modeled as a single homogenous reservoir, we will ensure that the optimization procedure cannot collapse the two-pool system into a single pool. This can be mitigated in the two-pool parallel optimization by constraining \(\gamma\) (i.e. the percentage of the inputs entering the fast pool) to a range of 50% to 95%. Similarly, for the two-pool series model structure we can constrain the range of the transfer coefficient to be between 0.0 and 0.1, ensuring that some carbon remains in the fast cycling pool.
Additionally, to enforce a relatively fast cycling pool and relatively slower cycling pool, we will loosely constrain the intrinsic decomposition rates as well (both model structures):
k1: [0.02, 1.00] (50 to 1 year) k2: [0.0001, 0.02] (10,000 to 50 years)
Finally, the models will be run to enforce steady-state, i.e. with unvarying carbon stocks. The amount of carbon observed in the system will be used in the cost function in addition to the radiocarbon observations made in 2001, 2009, and 2019. The inputs will be estimated from net ecosystem exchange (NEE) data measured at nearby eddy covariance sites: Blodgett experimental forest (AmeriFlux), Lower Teakettle (NEON), and Soaproot Saddle (NEON). Alternatively, using correlations between fluxes measured from these eddy covariance towers and GPP estimated from satellite retrievals of SIF, estimates can be made for inputs at the pixels corresponding to each site location.
cannot open compressed file '../data/derived/modFit_pars/pars.i.2ps_2021-04-07.Rdata', probable reason 'No such file or directory'Error in readChar(con, 5L, useBytes = TRUE) : cannot open the connection
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There were 19 warnings (use warnings() to see them)
There were 19 warnings (use warnings() to see them)
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ANpp_10-20 parameter fitting
time: 47.038957118988
ANrf_10-20 parameter fitting
time: 1.46544079780579
ANwf_10-20 parameter fitting
time: 1.1419420003891
BSpp_10-20 parameter fitting
time: 1.25985061327616
BSrf_10-20 parameter fitting
time: 1.00276673634847
BSwf_10-20 parameter fitting
time: 2.2469975511233
GRpp_10-20 parameter fitting
time: 52.5760071277618
GRrf_10-20 parameter fitting
time: 1.07178638378779
GRwf_10-20 parameter fitting
time: 52.5632190704346
$meanSystemAge
[,1]
[1,] 327.6551
$systemAgeDensity
[1] 0.035380011 0.028207779 0.022587252 0.018182443 0.014730120 0.012024044
[7] 0.009902635 0.008239299 0.006934854 0.005911594 0.005108636 0.004478282
[13] 0.003983162 0.003593998 0.003287850 0.003046745 0.002856605 0.002706396
[19] 0.002587475 0.002493072 0.002417880 0.002357743 0.002309405 0.002270313
[25] 0.002238470 0.002212308 0.002190601 0.002172387 0.002156913 0.002143590
[31] 0.002131954 0.002121643 0.002112374 0.002103923 0.002096118 0.002088821
[37] 0.002081926 0.002075348 0.002069023 0.002062897 0.002056932 0.002051096
[43] 0.002045363 0.002039714 0.002034135 0.002028613 0.002023139 0.002017706
[49] 0.002012307 0.002006938 0.002001596 0.001996279 0.001990982 0.001985706
[55] 0.001980449 0.001975209 0.001969986 0.001964779 0.001959587 0.001954410
[61] 0.001949249 0.001944101 0.001938968 0.001933849 0.001928744 0.001923653
[67] 0.001918576 0.001913512 0.001908461 0.001903424 0.001898401 0.001893391
[73] 0.001888394 0.001883410 0.001878439 0.001873482 0.001868538 0.001863606
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[85] 0.001829451 0.001824623 0.001819807 0.001815005 0.001810215 0.001805438
[91] 0.001800673 0.001795921 0.001791181 0.001786454 0.001781740 0.001777038
[97] 0.001772348 0.001767671 0.001763006 0.001758353 0.001753713
$quantilesSystemAge
[1] 1.703039 207.147766 1078.501105
$poolAgeDensity
[,1] [,2]
[1,] 2.440208e-01 0.0000000000
[2,] 1.911833e-01 0.0005713993
[3,] 1.497866e-01 0.0010175663
[4,] 1.173535e-01 0.0013656214
[5,] 9.194313e-02 0.0016368126
[6,] 7.203481e-02 0.0018477872
[7,] 5.643721e-02 0.0020115876
[8,] 4.421694e-02 0.0021384323
[9,] 3.464271e-02 0.0022363273
[10,] 2.714157e-02 0.0023115450
[11,] 2.126464e-02 0.0023689994
[12,] 1.666024e-02 0.0024125408
[13,] 1.305282e-02 0.0024451856
[14,] 1.022651e-02 0.0024692972
[15,] 8.012179e-03 0.0024867270
[16,] 6.277313e-03 0.0024989257
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[20,] 2.365192e-03 0.0025147570
[21,] 1.853060e-03 0.0025136587
[22,] 1.451819e-03 0.0025113642
[23,] 1.137459e-03 0.0025081362
[24,] 8.911665e-04 0.0025041805
[25,] 6.982034e-04 0.0024996586
[26,] 5.470224e-04 0.0024946968
[27,] 4.285764e-04 0.0024893941
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[29,] 2.630719e-04 0.0024780593
[30,] 2.061093e-04 0.0024721356
[31,] 1.614808e-04 0.0024660942
[32,] 1.265156e-04 0.0024599641
[33,] 9.912132e-05 0.0024537684
[34,] 7.765871e-05 0.0024475249
[35,] 6.084338e-05 0.0024412476
[36,] 4.766905e-05 0.0024349475
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[39,] 2.292482e-05 0.0024159872
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[41,] 1.407188e-05 0.0024033478
[42,] 1.102492e-05 0.0023970382
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[52,] 9.607416e-07 0.0023346322
[53,] 7.527136e-07 0.0023284732
[54,] 5.897295e-07 0.0023223301
[55,] 4.620362e-07 0.0023162027
[56,] 3.619921e-07 0.0023100912
[57,] 2.836105e-07 0.0023039956
[58,] 2.222007e-07 0.0022979159
[59,] 1.740879e-07 0.0022918521
[60,] 1.363929e-07 0.0022858042
[61,] 1.068599e-07 0.0022797722
[62,] 8.372168e-08 0.0022737560
[63,] 6.559354e-08 0.0022677556
[64,] 5.139066e-08 0.0022617711
[65,] 4.026311e-08 0.0022558022
[66,] 3.154500e-08 0.0022498492
[67,] 2.471460e-08 0.0022439118
[68,] 1.936318e-08 0.0022379900
[69,] 1.517050e-08 0.0022320839
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[94,] 3.400778e-11 0.0020893902
[95,] 2.664412e-11 0.0020838762
[96,] 2.087491e-11 0.0020783767
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[99,] 1.003908e-11 0.0020619653
[100,] 7.865332e-12 0.0020565236
[101,] 6.162263e-12 0.0020510964
$meanPoolAge
[,1]
[1,] 4.098012
[2,] 382.521968